A soccer ball of mass 0.45 kg is rolling with velocity 0, 0, 3.0 m/s, when you k

Question

A soccer ball of mass 0.45 kg is rolling with velocity 0, 0, 3.0 m/s, when you kick it. Your kick delivers an impulse of magnitude 1.5 N · s in the x direction. The net force on the rolling ball, due to the air and the grass, is 0.22 N in the direction opposite to the direction of the ball's momentum. Using a time step of 0.5 s, find the position of the ball at a time 1.5 s after you kick it, assuming that the ball is at the origin at the moment it is kicked. Use the approximation vavg pf/m. (Express your answer in vector form.) ...The answer is rf=<-4.45, 0, 4.01>m. Can someone show the steps to this question and answer in detail please. This all that was given in the question. The question must be answered with what is given above.

Explanation / Answer

This approach is an approximation (a good one) ...real computation needs calculus ...anyway :
equivalent mass me of an hollow sphere of mass m = 10*m/6 = 0.45*10/6 = 0.75 kg

Vo = I/m = 1.5 N*sec/0.75 kg = 2.0 m/sec
Eo = m/2*Vo^2 = 2^2*0.225 = 0.9 joule

after 2 meters
E1 = Eo-0.22*2 = 0.9 - 0.44 = 0.46 joule
V1 = Vo*E1/Eo = 2*0.46/0.9 = 1.43 m/sec
2*2 = (2 + 1.43)*t
t1 = 2*2 /(2+1.43) = 1.17 sec
a1 = -(2-1.43)/1.17 = -0.487 m/sec^2

after 4 meters
E2 = Eo-0.22*4 = 0.9-0.88 = 0.02 joule
V2 = Vo*E2/Eo = 2*0.02/0.9 = 0.298 m/sec
t2 = 2*2 /(1.17+0.298) = 2.72 sec
a2 = -(1.17-0.298)/2.72 = -0.32 m/sec^2

a = (a1+a2)/2 = -0.4035 m/sec^2

d(t) = Vo*t+a/2*t^2
after 1,5 sec :
d = 2*1.5 - 0.4035/2*2.25 = 2.91 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.